What exactly is the reason behind the tarqeeq raa in the word 'yasr' of surah fajr verse 4.

I hope you can continue to provide such vital information in the field of tajweed inshallah.

What exactly is the reason behind the tarqeeq raa in the word 'yasr' of surah fajr verse 4.

Also, does the letter dhad have a natural quality in it that allows for the cheeks to inflate slightly but involuntarily.

Jazakullah

Answer
Wa alikum assalaam wa rahmatullahi wa barakatuh
Ameen to your dua'. We apologize for the delay in answering your question.
Those who state there are two ways of reading the word "yasr" when stopping, with tarqeeq or tafkheem of the , look at the original word which actually has a which is part of the basic make up of the word on the end (not a pronoun or possesive). This is one of the many words in the Qur'an with a dropped in writing for no grammatical reason, and for Hafs 'an 'Aasim it is also dropped in pronunciation, although some of the different qira'aat read it with the .
Imam Ibn Al-Jazaree and the others who say there two allowed ways when stopping on the in this word are looking at the original make up of the word with the on the end, which would then leave the to be the next to last letter with a kasrah on it, thus read with tarqeeq . Since the is dropped in writing, then the would be the last letter and following the normal rules of takfheem and tarqeeq would have tafkheem when stopping on it.

No, the does not have a natural characteristic of blowing out of the cheeks and this should be avoided. Those who haev this tendency usually have a weakened sound of the .